Octahedral

Definitions

  • Webster's Revised Unabridged Dictionary
    • a Octahedral Having eight faces or sides; of, pertaining to, or formed in, octahedrons; as, octahedral cleavage; an octahedral crystal.
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Century Dictionary and Cyclopedia
    • octahedral Having eight equal surfaces or faces.
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Etymology

Webster's Revised Unabridged Dictionary
See Octahedron

Usage

In literature:

Brass was decomposed, and its constituent copper crystallized in cubic and octahedral forms aggregated in beautiful branches.
"The San Francisco Calamity" by Various
Acute rhombohedra in combination with the basal pinacoid are also frequent, giving crystals of octahedral aspect.
"Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 7" by Various
It crystallizes in the cubic system, the usual form being that of interpenetrating cubes twinned on an octahedral plane.
"Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 7" by Various
They were octahedral in form, with polished facets.
"Stories about Famous Precious Stones" by Mrs Goddard Orpen
It occurs as large octahedral crystals often with rounded edges, and as granular masses.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 1 "Franciscans" to "French Language"" by Various
A handful of small cubes and octahedral pebbles were passed up for inspection.
"Ande Trembath" by Matthew Stanley Kemp
From the latter deposit, by the application of heat, octahedral crystals of arsenic were readily obtained.
"Curiosities of Civilization" by Andrew Wynter
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In science:

AxB i | x = 0, 1, D , X, R, L} by UAB (·). O is the octahedral group, which is the (special) symmetry group of the octahedron and the cube.
A study of LOCC-detection of a maximally entangled state using hypothesis testing
Tr4) The octahedral axiom: For a composite A u−→ B v−→ C let Cu , Cv and Cvu be chosen as in (Tr1).
The characteristic cohomology class of a triangulated category
Axiom (Tr4) is a reformulation of Verdier’s octahedral axiom as described in Weibel [We].
The characteristic cohomology class of a triangulated category
We point out that the exact sequence (3.6) is the analogue of the exact triangle (#) in the octahedral axiom (1.3).
The characteristic cohomology class of a triangulated category
We prove now that the octahedral axiom holds provided (A, t, ∇) is cohomologically triangulated.
The characteristic cohomology class of a triangulated category
This section contains the results which allow us to prove the octahedral axiom for cohomologically triangulated categories.
The characteristic cohomology class of a triangulated category
As the octahedral tilts break the tetragonal symmetry of the planes, they allow spin-orbit effects, in the form of Dzyalozhinsky-Moriya (DM) antisymmetric exchange, to cause a slight canting of the spins along the c axis.
Neutron Scattering Studies of Antiferromagnetic Correlations in Cuprates
Within the localized picture the estimation of the strength of the octahedral crystal-field interactions is decisive.
Comment on a Phys. Rev. Lett. paper: the origin of the excited state in LaCoO3
The Ti ions have a 3d1 configuration, and the octahedral crystal field induces a splitting between the higher energy eg and lower energy t2g levels.
Theory of Raman and Resonant Inelastic X-ray Scattering from Collective Orbital Excitations in YTiO$_3$
Of these 22 families, the polyhedra in four have tetrahedral symmetry, in two have octahedral symmetry, and in sixteen have icosahedral symmetry.
Regular Polyhedra of Index Two, I
Figure 3 contains only two diagrams, since for octahedral symmetry the structures in the related families are also Petrie duals of each other.
Regular Polyhedra of Index Two, I
Figure 3: The two families of polyhedra with octahedral symmetry; from left to right, derived by Lemma 7.3 from the Petrie-dual of the octahedron, and the octahedron itself.
Regular Polyhedra of Index Two, I
The resulting potential is symmetric under the octahedral group, which in addition to the tetrahedral group of transformations includes the exchanges of the doublets, e.g. φ1 ↔ φ2 , and the C P -transformation φi → φ† i , separately, as well as their compositions with other transformations.
Frustrated symmetries in multi-Higgs-doublet models
Finally, we note that the octahedral symmetry can be implemented in a slightly different fashion described in .
Frustrated symmetries in multi-Higgs-doublet models
The ILD detector is an octahedral barrel with two endcaps (see ).
Tests of a particle flow algorithm with CALICE test beam data
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